The Mac Book Air has light sensors for automatically turn on and off the keyboard back-lightening.
If you are in a bright environment,then the back-light will not work.
Try taking your MBA to a darker environment,surely it will work.
The lights will be turned on automatically.
If this doesn't work,then try pressing F5 and F6.
If still you get no result,contact Apple Costumer support.

Well dear i think it is not a problem.it all depends upon where you are working on your mac.if you are working at bright place it will be turned off.if you ard working at dark place it will be turned on.so take your mac to the dark place.i think it will work.if does not work then press f5 i think then it will work.
Thanks

Hello friend
here this is a step to fix backlight problem
-You can find keyboard settings option in general settings of Macbook
-Then click on the keyboard settings you can find backlight option
-Then click it you can adjust the keyboard light here..........
-Now click on SAVE............Then it's done .................

That is a little minor issue which can be solved easily.
Either the keyboard light may be damaged and because of light effects, or it can be due to the wire un-plugged from inside your MacBook.
Check the wire first after opening the MacBook safely and if it is un-plugged, then plug-in once again.

If the problem still continues, then the Keyboard lights would be definitely damaged.
So, if it is some internal error, then replace your keyboard from your service center and if you don't want to replace or cant' do this, then work in a lighter place where you can see the keys.

Also check your Keyboard cable or its socket whether it might be damaged or not.
This can sort the issue,